Two-Dimensional Semiconducting Boron ... - ACS Publications

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Two-Dimensional Semiconducting Boron Monolayers Shao-Gang Xu, Xiao-Tian Li, Yujun Zhao, Ji-Hai Liao, Wang-Ping Xu, Xiao-Bao Yang, and Hu Xu J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b08680 • Publication Date (Web): 16 Nov 2017 Downloaded from http://pubs.acs.org on November 16, 2017

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Journal of the American Chemical Society

Two-Dimensional Semiconducting Boron Monolayers Shao-Gang Xu,†,‡,# Xiao-Tian Li, †,# Yu-Jun Zhao, † Ji-Hai Liao, † Wang-Ping Xu,‡ Xiao-Bao Yang, †,* and Hu Xu‡,* †

‡

Department of Physics, South China University of Technology, Guangzhou 510640, People’s Republic of China Department of Physics, South University of Science and Technology of China, Shenzhen 518055, People’s Republic of China

Supporting Information ABSTRACT: The two-dimensional boron monolayers were reported to be metallic both in previous theoretical predictions and experimental observations. Unexpectedly, we have firstly found a family of boron monolayers with the novel semiconducting property as confirmed by the first-principles calculations with the quasi-particle G0W0 approach. We demonstrate that the connected network of hexagonal vacancies dominates the gap opening for both the in-plane(s+px,y) and pz orbitals, with which various semiconducting boron monolayers are designed to realize the band-gap engineering for the potential applications in electronic devices. The semiconducting boron monolayers in our predictions are expected to be synthesized on the proper substrates, due to the similar stabilities to the ones observed experimentally.

Graphene1, a free-standing two-dimensional (2D) carbon(C) exfoliated from the bulk phase, has provoked a rush of attentions. However, the intrinsic metallicity of graphene prevents its application to practical nano-devices, and various means have been proposed to introduce a suitable band gap for graphene, such as the chemical functionalization (hydrogenated graphene)2 and physical cutting (graphene nanoribbons)3. Recently, the few-layer black phosphorus is attractive due to their semiconducting characteristic4, where the atomic structures can be theoretically determined through the relaxation from the layered bulk counterpart5. Boron(B), one of C’s nearest neighbors in the periodic table, demonstrates the polymorphism in low-dimensional structures6-8 due to the multi-centre bonds, leading to the diverse properties. Experimental observations show that small Bn clusters are planar triangular fragments9, however, the corresponding boron monolayers have been found to be not stable due to the large deformation and buckling10. Inspired by the computational prediction of B80,11 the stable boron monolayers with hexagonal vacancies have been proposed12,13, leading to extensive searches focusing on the concentration and distribution of vacancies14,15. Further experimental observation of B36 confirms that hexagonal vacancies are important in stabilizing the larger planar B clusters to be consid－ ered as the precursor for boron monolayers16. In addition, the B35 with a double-hexagonal vacancy may be another flexible motif to build various boron monolayers17,18, which are supposed to be synthesized on the proper metal surfaces19. Recently, two research groups have independently reported that the boron monolayers could be fabricated on the silver (Ag) substrates by the molecular beam epitaxy (MBE) method20,21. Theoretically, the detailed atomic structures of boron monolayers are confirmed by the first-

principles calculations22,23, where a penetration mechanism of initial nucleation is especially proposed.22 As is known, the polymorphism of boron monolayers will induce the variety of properties, including the unusual Dirac fermions24, and the coexisting Dirac nodal lines and tilted semi-Dirac cones25. During the growth of boron monolayers, the metallic B nanoribbons (BNRs) have been found across the steps on the Ag substrates26. To our knowledge, there are only few B periodical structures predicted to be semiconducting. In addition to the onedimensional (1D) B nanotubes with small diameters13, only one intrinsic BNR with armchair edges27 has been predicted to be semiconducting, and the 1D B chains28 will undergo a metalsemiconductor transition due to the mechanism of spin density wave. Till now, the planar boron monolayers are concluded to be metallic7,14,29 by experiments and theories, characterized by the out-of-plane pz-derived bands. However, it is not clear whether there are any semiconducting boron monolayers, the confirmation of which will extend our understanding of 2D boron. In this work, we have theoretically shown that the in-plane (s+px,y) orbitals and pz-derived bands in boron monolayers could be effectively modulated by the connected network of hexagonal vacancies, which results in a family of semiconducting boron monolayers as confirmed by the first-principles calculations and the quasi-particle G0W0 approach. We have found a simple rule to construct semiconducting boron monolayers for the realization of band-gap engineering, indicating a brand new platform for the potential applications in electronic devices. The first-principles calculations were performed based on density-functional theory (DFT) with the projected augmented wave (PAW)30 scheme, as implemented in Vienna ab initio simulation package (VASP)31(details in the Supporting Information). The Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional32 and the quasi-particle G0W0 approach33 were applied for the band gap corrections. Thermal stability was studied using ab initio molecular dynamics (AIMD) simulations with the temperature controlled by a Nosé heat bath scheme34. The climbing image nudged elastic band method (CI-NEB)35 was adopted to study the migration pathways of B atoms in boron monolayers. As shown in Figure 1a, the first semiconducting boron monolayer (β ) possesses the connected network of hexagonal vacancies which can be divided into the triangle regions (TriRs) and the heptagon regions(HepRs), where the real space structural parameters after relaxation are listed in Table S1. The HSE06 band structure calculation(see Figure 1b) confirms that this boron monolayer is semiconducting with an indirect gap of 0.741 eV. The projected

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band structure reveals that the valence band maximum (VBM) is dominated by the out-of-plane pz orbitals while the conduction band minimum (CBM) is attributed to the in-plane s+px,y orbitals. According to the calculated phonon dispersion (see Figure S1b), no imaginary phonon modes are found in the whole first Brillouin zone, indicating the kinetic stability of the new boron monolayer. We also assessed the thermal stability of the boron monolayer by performing AIMD simulation at the temperature of 500 K with the time step of 1 fs. The structural snapshot of the supercell at 10 ps (shown in Figure S1c) reveals that the semiconducting boron monolayer has a good thermodynamic stability, which can maintain the structural integrity in room-temperature environment. In addition, we have found three semiconducting boron monolayers assembled by the triangle regions and irregular polygon regions shown in Figure 1c, and the corresponding band structures are shown in Figure S2.

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The HSE06 band structures (shown in Figure S6) show that the above boron monolayers are semiconducting with the band gaps of 0.602, 0.416 and 0.396 eV, respectively. The β boron monolayer is an indirect gap semiconductor with the VBM is along MΓ, and the CBM is located at Γ point. Notably, the β boron mon olayer is a semiconductor with a direct gap, where both the VBM and CBM is located at Y point. The β, boron monolayer is an indirect gap semiconductor with the VBM is along Γ-X, and the CBM is located at Y point. Checking the projected orbitals plotted in the band structures, we can see that, the VBM and CBM are contributed by the in-planes+px,y orbitals for the β , β and β, boron monolayers. Similar to the α sheet12, there are gaps for inplane s+px,y orbitals near the Fermi level(EF) in a few previously proposed stable boron monolayers, while the pz orbitals account for their metallicity. Interestingly, our proposed boron monolayers open the energy gaps of s+px,y and pz orbitals near the EF level. As the number of β-UC in the HepRs increases, the band structures and the PDOS analysis (shown in Figure S7) indicate that the systems become metallic gradually, where the bands near the EF level are attributed to the in-plane s+px,y orbitals rather than the pz orbitals. The connected network of hexagonal vacancies is dominant to the gap opening for both s+px,y and pz orbitals in the semiconducting boron monolayers. Since the charge distributions of the valence bands (shown in Figure S8) are moving from the TriRs chains to the β BNRs regions with the increasing of the number of β-UC, which leads to the closing of the energy gaps for s+px,y and pz orbitals in β boron monolayers with m ≥ 6. By the combinations ( β,, ....(mi=1~5)) in the HepRs, we have constructed a family of semiconducting boron monolayers with various band gaps (shown in Table S2), indicating the realization of the band-gap engineering. As shown in Figure 2b, at a fixed vacancy concentration we can construct different structures with various band gaps, and the average formation energy (Eform) of a few semiconducting boron monolayers are in the region between the experimentally21 synthesized β12 (-5.925 eV/atom) and χ3 (5.940 eV/atom) sheets. There is a variation of boron monolayers' stabilities as a function of the metal substrates(shown in Figures S9-S11). In addition, the differences

In the heptagon region of β , there is a unit cell of β sheet12. Thus, we can construct a family potential semiconducting boron monolayers by increasing the number of β unit cell (β-UC) included in the HepRs (shown in Figure 2a). The named β boron monolayer is one with m β-UC in the heptagon regions, where there is one β-UC in the HepRs of the β boron monolayer (shown in Figure 1a) with the least number of atoms. Under the above definition, we can obtain the β boron monolayer with two β-UC assembled in the HepRs, as well as the β boron monolayer in the similar way. Furthermore, the β, boron monolayer is the hybrid structure of β and β . The structural parameters of these three new boron monolayers with the same space group of Pm(6) are presented in Table S1. There are no imaginary phonon modes along all the high-symmetry lines (see Figure S3), and the calculated diffusion barriers of the B atoms in the TriRs are larger than 1 eV (shown in Figure S4). Furthermore, the AIMD simulations in Figure S5 show that the semiconducting boron monolayers can maintain their frameworks at 700 K, which indicate that the boron monolayers should have high dynamic and thermal stabilities.

Figure 1. The atomic structures and band structure for the semiconducting boron monolayers. (a,b) represent the atomic structure and HSE06 band structure of the β boron monolayer. (VBM is set to 0.) (c) represents the atomic structures of the three semiconducting boron monolayers (β , β , β ). The blue solid lines represent the connecting lines of the hexagonal vacancies. The black dash lines represent the unit cells of the corresponding boron monolayers.

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The direct band gap characteristic of β boron monolayer can be potentially applied in the infrared optoelectronic devices and field-effect transistor. The G0W0 calculation (shown in Figure 3a) predicts that the fundamental band gap of β boron monolayer is 0.484 eV, which maintains the characteristic of direct gap at Y point with a linear increasing as the biaxial strain (－3% ≤ σ ≤ 3%). The semiconducting characteristic in boron monolayers is expected to be robust against the strain induced by the substrate and the band gaps could be effectively modulated by means of the biaxial strain. As shown in Figure 3b, the band decomposed charge distributions of VBM and CBM for β are found to be mainly contributed to the in-plane sp2 hybrid orbitals, which are located in TriRs. Therefore, we confirm that the vanished metallicity characterized by the gap opening in both in-plane sp2 and pz orbitals is attributed to the connected network of hexagonal vacancies with the motif of TriRs. In summary, we have demonstrated a family of boron monolayers with the novel semiconducting property for the first time, attributed to both the in-plane s+px,y and the pz-derived bands modulated by the connected network of hexagonal vacancies. The proposed semiconducting boron monolayers may be synthesized on the proper substrates, since they are of similar stability to those observed experimentally. For the boron monolayer with a direct gap, mechanical biaxial strains within a small region may induce a linear tuning of the band gaps, indicating a brand new platform for the potential applications in electronic devices.

Figure 2. The combination rule and atomic structures of the semiconducting boron monolayers. (a) Schematic diagram of the combination rule for the semiconducting boron monolayers ( β (m=1~3) and β, ). The blue solid lines represent the connecting lines of the hexagonal vacancies. The black dash lines represent the unit cells of the corresponding boron monolayers. The red dash lines represent the unit cell of β sheet. (b) The relationship of band gaps and average formation energy (Eform) for the new designed semiconducting boron monolayers. The inset represents the average adsorption energy (Ead) of boron monolayers on the Ag/Au(111) substrates. of the average adsorption energy between semiconducting (β , β ) and (β12, χ3) on the Ag(111) substrate are about 40 meV/atom, which will be reduced to be within 30 meV/atom for Au(111) substrate(shown in the inset of Figure 2b). Note that the semiconducting boron monolayers are more stable than the experimental metastable α sheet36 on both Ag(111) and Au(111) substrates, indicating the possible synthesis by the control of growth conditions. On the Cu(111) substrate, β is of similar stability to χ3 and it will become more stable than β12 on the Ni(111) substrate(as shown Figure S11), though the larger adsorption energy might induce difficulty in the exploitation from the substrates. It is expected that the Au-Cu alloys might be a suitable substrate to synthesize the semiconducting boron monolayers to avoid the larger adhesion energy of boron monolayers on substrates.

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Figure 3. The relation of band gaps and biaxial strain for β boron monolayer. (a) The G0W0 band structure of β boron monolayer (VBM is set to 0), and the inset represents the relation of G0W0 band gaps and biaxial strain. (b) The band decomposed charge densities of β boron monolayer at VBM and CBM.

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Supporting Information The Supporting Information is available free of charge on the ACS Publications website. AIMD simulation results; Phonon dispersion spectras; NEB diffusion path; Band structures; PDOS analysis; Band decomposed charge densities; Adsorption on the metal substrates; Tables of stabilities and band gaps

AUTHOR INFORMATION Corresponding Author *[email protected]; [email protected]

ORCID Xiao-Bao Yang: 0000-0001-8851-1988 Hu Xu: 0000-0002-2254-5840

Author Contributions #S.X. and X.L. contributed equally to this work.

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (Nos. 11474100, 11674148, 11574088), Guangdong Natural Science Funds for Distinguished Young Scholars (Nos. 2014A030306024, 2017B030306008), the Basic Research Program of Science, Technology and Innovation Commission of Shenzhen Municipality (Grant No. JCYJ20160531190054083), and Guangdong Natural Science Funds for Doctoral Program (Grant No. 2017A030310086).

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Two-Dimensional Semiconducting Boron ... - ACS Publications

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